On the one hand it can be a good strategy to show non available products with the note "Product currently not available". On the other hand it can be frustrating for your customers to find a lot of interesting products which they are not able to purchase. In case you rather want to automatically hide products which are dropping under an inventory of 1 this is what you have to do:
- Hit "Store settings > Main Settings"
- Tick "Hide unavailable products"
- Save and you're done :-)